Subadditivity of Kodaira dimensions for fibrations of three-folds in positive characteristics

Abstract

In this paper, we will prove subadditivity of Kodaira dimensions for a fibration with possibly singular geometric generic fiber, under certain nefness and relative semi-ampleness conditions. As an application, for a fibration $f:X\to Y$ of a smooth projective threefold over an algebraically closed field of characteristic $p>5$, under the assumption that $Y$ is of general type and non-uniruled, we prove subadditivity of Kodaira dimensions when general fibers are smooth or when $K_{X/Y}$ is relatively big over $Y$.

24 pages, accepted by Adv. Math., welcome comments

References in corpus (1)

• Iitaka's $C_{n,m}$ conjecture for 3-folds over finite fields

Cited by in corpus (1)

• Abundance for non-uniruled 3-folds with non-trivial Albanese maps in positive characteristics